Contents 1 Introduction
Extensive works have been devoted in the past to the obtaining of decision error probabilities for linear equalizer systems [1]–[7]. Aaron and Tufts gave an error probability based on the conditional error probability concept [1]. Saltzberg derived an upper bound for the error probability using the worst-case sequence [2]. Lugannani evaluated an error bound by the Chernoff inequality [3]. Ho and Yeh evaluated the error probability in terms of the first 2k moments of the ISI [4]. Glave derived an error bound for correlated binary signals. And Yao and Tobin obtained upper and lower bounds for the error probability from the theory of moment spaces [6]. Most of these results are either too complicated or tedious, or limited to special cases only (e.g., binary transmissions only or MSE case only), or just give the bounds only. In this work, a generalized formula of decision error probability is derived for any linear equalizer system (any algorithm) in bandlimited channels employing M-ary PAM transmission. The approach is close to but goes beyond that of Aaron and Tufts. The resultant mathematical expression will be in terms of equalizer tap weight coefficients and valid for any assignment of tap weights (non-optimum or optimum state).
